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Find the surface area of the cube shown below.

Find the surface area of the cube shown below.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question

Find the surface area of the cube shown below. 

### Calculating the Surface Area of a Cube #### Problem Statement: Find the surface area of the cube shown below. #### Input box for answer: `__________ units^2` #### Diagram: A cube is shown with dimensions clearly marked. The side length of the cube is given as \( \frac{2}{3} \) units. --- **Explanation:** To find the surface area of a cube, you can use the following formula: \[ \text{Surface Area} = 6 \times \text{side length}^2 \] For the given cube: - Side length (\( s \)) = \( \frac{2}{3} \) units Plugging in the side length value: \[ \text{Surface Area} = 6 \times \left( \frac{2}{3} \right)^2 \] First, square the side length: \[ \left( \frac{2}{3} \right)^2 = \frac{4}{9} \] Then, multiply by 6: \[ \text{Surface Area} = 6 \times \frac{4}{9} = \frac{24}{9} = \frac{8}{3} \] Thus, the surface area of the cube is: \[ \frac{8}{3} \text{ units}^2 \]
Transcribed Image Text:### Calculating the Surface Area of a Cube #### Problem Statement: Find the surface area of the cube shown below. #### Input box for answer: `__________ units^2` #### Diagram: A cube is shown with dimensions clearly marked. The side length of the cube is given as \( \frac{2}{3} \) units. --- **Explanation:** To find the surface area of a cube, you can use the following formula: \[ \text{Surface Area} = 6 \times \text{side length}^2 \] For the given cube: - Side length (\( s \)) = \( \frac{2}{3} \) units Plugging in the side length value: \[ \text{Surface Area} = 6 \times \left( \frac{2}{3} \right)^2 \] First, square the side length: \[ \left( \frac{2}{3} \right)^2 = \frac{4}{9} \] Then, multiply by 6: \[ \text{Surface Area} = 6 \times \frac{4}{9} = \frac{24}{9} = \frac{8}{3} \] Thus, the surface area of the cube is: \[ \frac{8}{3} \text{ units}^2 \]
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